1,841 research outputs found
Proximal Iteratively Reweighted Algorithm with Multiple Splitting for Nonconvex Sparsity Optimization
This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for
solving a general problem, which involves a large body of nonconvex sparse and
structured sparse related problems. Comparing with previous iterative solvers
for nonconvex sparse problem, PIRE is much more general and efficient. The
computational cost of PIRE in each iteration is usually as low as the
state-of-the-art convex solvers. We further propose the PIRE algorithm with
Parallel Splitting (PIRE-PS) and PIRE algorithm with Alternative Updating
(PIRE-AU) to handle the multi-variable problems. In theory, we prove that our
proposed methods converge and any limit solution is a stationary point.
Extensive experiments on both synthesis and real data sets demonstrate that our
methods achieve comparative learning performance, but are much more efficient,
by comparing with previous nonconvex solvers
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
Maximum Entropy Vector Kernels for MIMO system identification
Recent contributions have framed linear system identification as a
nonparametric regularized inverse problem. Relying on -type
regularization which accounts for the stability and smoothness of the impulse
response to be estimated, these approaches have been shown to be competitive
w.r.t classical parametric methods. In this paper, adopting Maximum Entropy
arguments, we derive a new penalty deriving from a vector-valued
kernel; to do so we exploit the structure of the Hankel matrix, thus
controlling at the same time complexity, measured by the McMillan degree,
stability and smoothness of the identified models. As a special case we recover
the nuclear norm penalty on the squared block Hankel matrix. In contrast with
previous literature on reweighted nuclear norm penalties, our kernel is
described by a small number of hyper-parameters, which are iteratively updated
through marginal likelihood maximization; constraining the structure of the
kernel acts as a (hyper)regularizer which helps controlling the effective
degrees of freedom of our estimator. To optimize the marginal likelihood we
adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be
significantly computationally cheaper than other first and second order
off-the-shelf optimization methods. The paper also contains an extensive
comparison with many state-of-the-art methods on several Monte-Carlo studies,
which confirms the effectiveness of our procedure
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